Random threshold driven tail dependence measures with application to precipitation data analysis

Abstract

This paper first studies the theoretical properties of the tail quotient correlation coefficient (TQCC) which was proposed to measure tail dependence between two random variables. By introducing random thresholds in TQCC, an approximation theory between conditional tail probabilities is established. The new random threshold-driven TQCC can be used to test the null hypothesis of tail independence under which TQCC test statistics are shown to follow a Chi-squared distribution under two general scenarios. The TQCC is shown to be consistent under the alternative hypothesis of tail dependence with a general approximation of max-stable distribution. Second, we apply TQCC to investigate tail dependencies of a large scale problem of daily precipitation in the continental US. Our results, from the perspective of tail dependence, reveal nonstationarity, spatial clusters, and tail dependence from the precipitations across the continental US.

Assessing the features of extreme smog in China and the differentiated treatment strategy

“…This kind of dependence, i.e. extreme dependence [52][53][54], should be explored in future studies so that the co-movement of extreme smog in different areas can be determined.…”

The tail dependence of the carbon markets: The implication of portfolio management

“…The basic notion of tail dependence is that the probability of a two-dimensional random vector occurs extremal values at the same time. Zhang et al [44] states that the identically distributed random variable pair (X, Y) is tail dependence if…”

“…Contrary to the former hypothesis, the tail quotient correlation and the tail independence test statistics based on the null hypothesis of tail independence were generated [48]. Tail quotient correlation coefficient (TQCC) was first proposed to measure tail dependence between two random variables using random thresholds which can diverge to infinity [44]. A practically workable threshold selection was also suggested in the paper.…”

“…The basic notion of tail dependence is that the probability of a two-dimensional random vector occurs extremal values at the same time. Zhang et al [ 44 ] states that the identically distributed random variable pair (X, Y) is tail dependence if where T F = sup{t ∈ R: P(T ≤ t) < 1}. λ is called the bivariate upper tail dependence index which quantifies the degree of dependence of the bivariate tails.…”

Random Threshold Driven Tail Dependence Measures with Application to Precipitation Data Analysis

“…The data units are tenths of a millimeter. The data were obtained from Dr. Pavel Groisman of the National Climatic Data Center (NCDC), the same as used by Smith, Grady, and Hegerl (2007) and Shamseldin et al (2008). References include Smith et al (2007), Karl and Knight (1998), Groisman et al (1999), andHegerl et al (2006), among others.…”